The occurrence of repetitive genomic changes that provide a selective growth advantage in pluripotent stem cells is of concern for their clinical application. However, the effect of different culture conditions on the underlying mutation rate is unknown. Here we show that the mutation rate in two human embryonic stem cell lines derived and banked for clinical application is low and not substantially affected by culture with Rho Kinase inhibitor, commonly used in their routine maintenance. However, the mutation rate is reduced by >50% in cells cultured under 5% oxygen, when we also found alterations in imprint methylation and reversible DNA hypomethylation. Mutations are evenly distributed across the chromosomes, except for a slight increase on the X-chromosome, and an elevation in intergenic regions suggesting that chromatin structure may affect mutation rate. Overall the results suggest that pluripotent stem cells are not subject to unusually high rates of genetic or epigenetic alterations.